Endoluminal grafts, or endografts, are tubular grafts, widely used to repair body lumens, which are introduced to a lumen site in need of repair endoluminally from a distal lumen location. One application for such endografts is to exclude aneurysms in various body lumens. For procedural success, it is important to deploy the endograft such that its proximal and distal ends are fixed to relatively healthy tissue. It is also important to deploy the endograft such that it does not interfere with branch lumens or extend beyond the repair area. Thus, precise placement in the lumen is important. It is also desirable to maintain a flow of fluid during delivery and deployment of the endograft. Repair of aneurysms in high-pressure lumens, such as the thoracic aorta, is complicated by the force of fluid pressure acting on the endograft during deployment. This force makes it difficult to accurately place the endograft. Typically, the expansion of the endograft from a compressed configuration (in which it is delivered to the repair site) to its expanded deployed configuration is not instantaneous, but occurs longitudinally from one end of the graft to the other. As this occurs, fluid flow within the lumen causes a windsock effect, which applies longitudinal force to the endograft. This problem is exacerbated because typical endografts cannot be repositioned after deployment. It is believed that an endograft less susceptible to this problem would be useful.